Philips Technical Review, vol. 41, no. 11/12, 1983/84, pp. 348-361, discloses a device of the kind described in the opening paragraph in which a shaft is supported by five pairs of electromagnets in such a way that rotation of the shaft is possible only about the centerline of the shaft. A force exerted on the shaft by an electromagnet is substantially directly proportional to the square of the value of the current through the electromagnet and substantially inversely proportional to the square of the size of an air gap between the electromagnet and the shaft. As a result of the relation between the electromagnetic force and the size of the air gap, the position of the shaft relative to the electromagnets is not stable unless additional measures are taken. To maintain a stable desired position of the shaft in the known device, the position of the shaft relative to each pair of electromagnets is measured by means of a position sensor, and a control current determined from the difference between the measured and the desired position is passed through the two electromagnets of the relevant pair. The value of the control current is thereby determined by means of a control unit having a proportional, differentiating and integrating action (PID controller). A stable support is obtained through the electromagnets controlled by the PID controller.
Since there is a non-linear relation between the electromagnetic force and the size of the air gap and the value of the current, the known device constitutes a non-linear system. The PID controller used is a linear control unit which in the known device is optimized for a working point determined by a desired size h.sub.0 of the air gap and by a basic current i.sub.0 through the electromagnets. As a result, however, a number of characteristics of the support which also determine the stability of the support, such as stiffness and bandwidth, are dependent on the position of the shaft relative to the electromagnets, whereas the PID controller used functions optimally only in the case of relatively small displacements of the shaft from the desired position. It is a disadvantage of the known device, accordingly, that only one position of the shaft is optimally stable, whereas any other position of the shaft is less stable, or may even be unstable. Stability problems can thus occur, especially upon switching on of the support device.